@article{EJP374,
author = {Jean-René Chazottes and Cristian Giardina and Frank Redig},
title = {Relative entropy and waiting times for continuous-time Markov processes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {continuous-time Markov chain, law of large numbers, central limittheorem, large deviations, entropy production, time-reversed process},
abstract = {For discrete-time stochastic processes, there is a close connection between return (resp. waiting) times and entropy (resp. relative entropy). Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one needs a reference measure on path space and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-time Markov processes with finite state space. A reference measure of special interest is the one associated to the time-reversed process. In that case relative entropy is interpreted as the entropy production rate. The main results of this paper are: almost-sure convergence to relative entropy of the logarithm of waiting-times ratios suitably normalized, and their fluctuation properties (central limit theorem and large deviation principle).},
pages = {no. 40, 1049-1068},
issn = {1083-6489},
doi = {10.1214/EJP.v11-374},
url = {http://ejp.ejpecp.org/article/view/374}}